Simplify the following expression: $ x = \dfrac{-4z}{-10z + 4} + \dfrac{-3}{2} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-4z}{-10z + 4} \times \dfrac{2}{2} = \dfrac{-8z}{-20z + 8} $ Multiply the second expression by $\dfrac{-10z + 4}{-10z + 4}$ $ \dfrac{-3}{2} \times \dfrac{-10z + 4}{-10z + 4} = \dfrac{30z - 12}{-20z + 8} $ Therefore $ x = \dfrac{-8z}{-20z + 8} + \dfrac{30z - 12}{-20z + 8} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-8z + 30z - 12}{-20z + 8} $ $x = \dfrac{22z - 12}{-20z + 8}$ Simplify the expression by dividing the numerator and denominator by -2: $x = \dfrac{-11z + 6}{10z - 4}$